Question: Simplify the following expression: $n = \dfrac{r^2 - 6r - 7}{r - 7} $
Answer: First factor the polynomial in the numerator. $ r^2 - 6r - 7 = (r - 7)(r + 1) $ So we can rewrite the expression as: $n = \dfrac{(r - 7)(r + 1)}{r - 7} $ We can divide the numerator and denominator by $(r - 7)$ on condition that $r \neq 7$ Therefore $n = r + 1; r \neq 7$